I voted for "was" rather than "is" because in the most commonly occurring contexts that will be the correct choice.
The most commonly occurring context is reporting speech that happened clearly in the past: "In January I met a man who said his name was John."
Substitute "is" for "was" and it sounds plain wrong.
Contrast a situation where one police officer joins his colleague who has apprehended a nasty villain. He asks his colleague who this nasty villain is. The colleague replies, "He said his name was/is John Doe."
In the latter context, "is" is the more natural choice because the reported event is not, as dduck says, firmly in the past. However, this is no simple matter of whether the person whose speech is being reported is present.
If the two officers stepped into another room and had the discussion, I
would suggest that "is" remains the preferable option.
So, whilst there are examples where "is" is clearly the better option and examples where "was" is clearly the better option, there is a thin grey line between the two that has the potential for confusion.
Sounds sensible, thanks :D .
Tdol, what's your opinion? :wink: